Abstract
Biadjoint scalar field theory has been the subject of much recent study, due to a number of applications in field and string theory. The catalogue of exact non-linear solutions of this theory is relatively unexplored, despite having a role to play in extending known relationships between gauge and gravity theories, such as the double copy. In this paper, we present new solutions of biadjoint scalar theory, corresponding to singular line configurations in four spacetime dimensions, with a power-law dependence on the cylindrical radius. For a certain choice of common gauge group (SU(2)), a family of infinitely degenerate solutions is found, whose existence can be traced to the global symmetry of the theory. We also present extended solutions, in which the pure power-law divergence is partially screened by a form factor.
Highlights
To the best of our current experimental knowledge, the forces of nature are described by field theories, making the latter the subject of intense ongoing scrutiny
Double-copy-like ideas have a natural representation in terms of the so-called CHY equations [70,71], which themselves emerge from ambitwistor string theory [72], and have been investigated at loop level [73]
We have obtained new solutions of the biadjoint scalar field theory, which occurs in a number of contexts, including the double copy relationship between gauge theories and gravity
Summary
To the best of our current experimental knowledge, the forces of nature are described by (quantum) field theories, making the latter the subject of intense ongoing scrutiny. A number of intriguing relationships have been discovered between field theories whose physics is very different One such correspondence is the double copy [1,2,3], that relates (non-abelian) gauge theories and gravity. One may catalogue fully non-linear solutions of various field theories, before trying to match them up in some way How to do the latter is unclear, as all previous examples of how to perform the double copy involve solutions of the linearised biadjoint equation. They included a spherically symmetric monopole-like object in the case in which both Lie groups are the same, where the field aa has a power-law behaviour, diverging at the origin.
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